If x is the area, y is the circumference and z is the diameter of circle then the value of `(x)/(yz)` is

Options

A. `4:1`
B. `1:4`
C. `1:2`
D. `2:1`

Answer

To solve the problem, we need to find the value of \(\frac{x}{yz}\) where:

- \(x\) is the area of the circle,
- \(y\) is the circumference of the circle,
- \(z\) is the diameter of the circle.

### Step-by-Step Solution:

1. **Define the radius of the circle**:
Let the radius of the circle be \(R\).

2. **Calculate the area \(x\)**:
The area \(x\) of a circle is given by the formula:
\[ x = \pi R^2 \]

3. **Calculate the circumference \(y\)**:
The circumference \(y\) of a circle is given by the formula:
\[ y = 2\pi R \]

4. **Calculate the diameter \(z\)**:
The diameter \(z\) of a circle is given by the formula:
\[ z = 2R \]

5. **Substitute \(x\), \(y\), and \(z\) into the expression \(\frac{x}{yz}\)**:
We need to find:
\[ \frac{x}{yz} = \frac{\pi R^2}{(2\pi R)(2R)} \]

6. **Simplify the expression**:
First, calculate \(yz\):
\[ yz = (2\pi R)(2R) = 4\pi R^2 \]
Now substitute this back into the expression:
\[ \frac{x}{yz} = \frac{\pi R^2}{4\pi R^2} \]

7. **Cancel out common terms**:
The \(\pi\) and \(R^2\) in the numerator and denominator cancel out:
\[ \frac{x}{yz} = \frac{1}{4} \]

### Final Answer:
Thus, the value of \(\frac{x}{yz}\) is \(\frac{1}{4}\).

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